What is the first derivative and second derivative of f(x) = (x-1)^2 (x-3)?

1 Answer
Jun 27, 2018

f'(x)=3(x-1)^2-4(x-1)

f''(x)=6x-10

Explanation:

Let u=x-1 , x-3=u-2 therefore (du)/dx=1

u^2(u-2)=u^3-2u^2

color(blue)(d/dx)(u^3-2u^2)

3u^2*(du)/dx-4u(du)/dx

Substitute

f'(x)=3(x-1)^2-4(x-1)

color(blue)(d/dx)(3u^2-4u)

6u(du)/dx-4(du)/dx

Substitute

f''(x)=6(x-1)-4=6x-10